An atomic force microscope (AFM) is a comparatively high-resolution type of scanning probe microscope. With demonstrated resolution of fractions of a nanometer, AFMs promise resolution more than 1000 times greater than the optical diffraction limit.
Many known AFMs include a microscale cantilever with a sharp tip (probe tip) at its end that is used to scan the specimen surface. The cantilever is typically silicon or silicon nitride with a probe tip radius of curvature on the order of nanometers. When the probe tip is brought into contact with a sample surface, forces between the probe tip and the sample lead to a deflection of the cantilever. One or more of a variety of forces are measured via the deflection of the probe tip. These include mechanical forces and electrostatic and magnetostatic forces, to name only a few.
Typically, the deflection of the cantilevered probe tip is measured using a laser spot reflected from the top of the cantilever and onto an optical detector. Other methods that are used include optical interferometry and piezoresistive AFM cantilever sensing.
One component of AFM instruments is the actuator that maintains the angular deflection of the tip that scans the surface of the sample in contact-mode. Most AFM instruments use three orthonormal axes to image the sample. The first two axes (e.g., X and Y axes) are driven to raster-scan the surface area of the sample with respect to the probe tip with typical ranges of 100 μm in each direction. The third axis (e.g., Z axis) drives the probe tip orthogonally to the plane defined by the X and Y axes for tracking the topography of the surface.
Generally, the actuator for Z axis motion of the tip to maintain a near-constant deflection in contact-mode requires a comparatively smaller range of motion (e.g., approximately 1 μm (or less) to approximately 10 μm). However, as the requirement of scan speeds of AFMs increases, the actuator for Z axis motion must respond comparatively quickly to variations in the surface topography. In a contact-mode AFM, for example, a feedback loop is provided to maintain the tip of a cantilever in contact with a surface. The probe tip-sample interaction is regulated by the Z feedback loop, and the bandwidth of the Z feedback loop dictates how fast scanning can occur with the Z feedback loop remaining stable.
Conventionally, the signal that the Z feedback loop outputs to the Z actuator is imaged to create a topograph of a surface. However, this method of measuring topography is generally accurate only at low scan rates. Even if the probe tip tracks the sample surface perfectly at higher scan rates, the resulting image may still be distorted and full of ringing, thus leading to an unacceptable tradeoff between speed and image quality.
FIG. 6 is a simplified block diagram of a conventional AFM feedback loop, which includes controller 610, physical system 630 and sensor 650. The feedback loop regulates the distance between the probe tip and the sample surface as monitored by some relative height signal, which may be provided by cantilever deflection signal y (as shown in FIG. 6), or by resonant frequency, or by AC amplitude, for example, depending on the AFM mode. As the probe tip is scanned, the changing sample height h of the sample surface disturbs the deflection signal y as detected by sensor 650 from a deflection setpoint r, resulting in an error signal e. In response to the error signal e, the controller 610 adjusts the controller output signal u to change the probe height z of the probe tip, screening out the disturbance. However, the probe height z is not known and must be inferred from other signals in order to reconstruct the sample height h, which is the topography of the sample surface.
To address this issue, conventional AFMs scan the probe tip slowly, as mentioned above, to enable two approximations. The first approximation is that the probe tip tracks the sample surface perfectly, so that probe height z sample height h. The second approximation is that the desired physical system response P0 of the physical system 630 (including the piezoelectric actuator) is constant, so that that the probe height z is proportional to the controller output signal u, or probe height z≈P0u. Together, these two approximations lead to sample height h≈P0u, which enables maps of the controller output signal u to be calibrated into topographs. However, at higher frequencies, both the first and second approximations break down. As the bandwidth of the closed AFM loop is approached, the sample surface becomes poorly tracked, effectively negating the first approximation. Also, the physical system 630 possesses electromechanical resonances that amplify the probe tip motion at some frequencies and null it at other frequencies. This frequency dependence of the piezoelectric response P0 prohibits the probe height z from being directly inferred from controller output signal u, effectively negating the second approximation and otherwise introducing ringing artifacts into the topograph regardless of how well the sample is tracked.
Some conventional AFMs include a sensor that attempts to measure the actual extension of the piezoelectric actuator in the physical structure 630. However, such sensors typically have limited bandwidth and are otherwise oblivious to vibrations of the mechanical structures outside of the piezoelectric actuator that also affect probe-sample separation. When the sensor bandwidth is exceeded or the vibrational modes are excited, the sensor signal no longer reflects the probe height z, and thus image distortion and ringing artifacts still appear at moderate frequencies.